Republican presidential nominee Mitt Romney sounded more positive than ever about immigration in Tuesday’s town-hall debate, a turn of events that is causing Democrats to loudly assert that Romney is an extremist on the issue.

“Mitt Romney is the most extreme presidential candidate on immigration in modern history,” said Rep. Nydia Velazquez, D-N.Y., in a conference call organized on Wednesday by President Obama’s campaign.

Both Becerra and Velazquez pointed to Romney’s earlier statements that he would veto the Dream Act to legalize undocumented youth.

In actuality, Romney sounded more moderate in the debate than he has in the past. He backed away from his earlier statements on the Dream Act. He suggested for the first time on a national stage that undocumented children in the United States should “have a pathway to permanent residence,” perhaps by joining the military. "Permanent residence" is the legal term for a green card, which leads to U.S. citizenship. Romney made a similar statement about the Dream Act to a reporter in Iowa last year, and he suggested legalization (but not citizenship) for military service in a speech to the National Association of Latino Elected and Appointed Officials in June.

The Service Employees International Union, the labor group that has pushed the hardest for citizenship for undocumented immigrants, rejects this idea. “We heard him say that he would offer a pathway to citizenship for dreamers only if they serve in the military—so that, in his eyes, they are good enough to sacrifice their lives but not to earn legal status,” said SEIU International Secretary-Treasurer Eliseo Medina.

Romney didn't stop at the Dream Act in his positive comments. He also said that as president, he would not round up 12 million illegal immigrants; instead, he would allow them to choose to leave the country. He said the legal-immigration system should be cleaner and simpler. He also echoed his oft-repeated call for automatic green cards for college math and science graduates.

It was enough to agitate advocates for less immigration. Numbers USA President Roy Beck said his grassroots network would have to be on guard if Romney is elected to make sure any Dream Act compromise “doesn’t sell out the American unemployed workers.” A tradeoff would have to come from eliminating other visa categories, he said.

Beck sees what Democrats refuse to acknowledge — that Romney is looking for a compromise. “I doubt that many of the groups that are the most committed to the Dream Act would think that their best chances lie with Romney, but I actually think that’s the case,” he said.

Democrats have shown nothing but scorn for Romney’s attempts to soften his stance on immigration. And who can blame them? They thought they had alliances with Republicans like Sen. John McCain, R-Ariz., and President George W. Bush. But those guys failed them in the end.

“It’s the flavor of the month with Romney,” Becerra said of Romney’s waffling on the Dream Act. “If I had to base a decision on which parachute to choose when I’m getting ready to jump out of a plane, I would not choose Romney’s.”

Becerra has good reason to be skeptical. He has seen firsthand how difficult it is to negotiate with Republicans who want broad immigration overhaul badly enough to consider a path to citizenship for the undocumented population. He negotiated in secret with several House Republicans in 2009 and 2010 to craft just such a deal. Those Republicans feared retribution from voters for the talks, which is why they insisted on complete secrecy. Many of them lost their reelection fights anyway.

It makes sense that Democrats who have been burned several times by Republicans on immigration aren't easily persuaded by Romney's comments, particularly if they think he's simply doing it to get votes.

There are 23.7 million Hispanic votes at stake, some of them in key swing states like Florida and Colorado, according to the Pew Hispanic Center. Obama holds a commanding lead nationwide, with support from 65 percent to 70 percent of Latino voters, depending on the state.

Still, it would only take a few switchers in battleground states to tip the balance in a tight race. Hispanics tend to lean conservative on other issues, particularly in Florida. But they will stick with Democrats if they are turned off by harsh rhetoric from Republicans about illegal immigrants.

It's possible that all Romney needs to do is look reasonable on immigration to swing a few Hispanic votes. Immigration is not among the top issues of concern for Latinos, according to Pew. They care about education, jobs and the economy, and health care first. That makes them look a lot like the rest of the voting population: divided and dividable.